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Right now there isn't a way to reference a part studio from another document. What you can do is copy the part studio in the first document by right mouse clicking on the part studio tab at the bottom of the page. From there there is an option to "Copy to clipboard". After this, navigate to the document you want to copy it to and hit the plus sign (+) in the bottom left corner and choose "Paste Tab".

@Micah ,Onshape documents are like containers, in which they contain assembly studio and part studio tabs. Currently in Onshape document to document referencing is not available. User can use and copy part studio ofdifferent document. User have to use
"copy to clipboard" option to copy the part studio and "paste tab" option to paste in different document as shown in below video.